Value-added trade and international shock transmission in ...

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Value-added trade and international shock transmission in a New

Keynesian model of production fragmentation

Chin-Yoong Wonga,*

Yoke-Kee Enga

aDepartment of Economics, Faculty of Business and Finance, Universiti Tunku Abdul Rahman, Jalan

Universiti, Bandar Barat 31900 Kampar, Perak, Malaysia.

* Corresponding author. Tel: 6054688888, ext. 1035. Fax: 6054667407. Email address:

[email protected]

Abstract

This paper proposes a New Keynesian model of production fragmentation that allows the

decomposition of trade into value added components compatible with the most

comprehensive definition of value-added trade in the empirical trade literature. In so doing, a

country’s position in the value chains of production can be identified transparently. The

model is then estimated on ten East Asian economies by using Bayesian method. We find that

countries vertically bound but specialized in different value chains tend to respond uniformly

towards supply and demand shocks. The magnitude of the response is also shaped by the

country upstreamness in production sharing.

Keywords: Value-added trade; Production fragmentation; Vertical specialization; New

Keynesian; Bayesian estimation

JEL classification: F14, F41, F44,

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1. Introduction

One of the defining characteristics of today’s international trade is the heavy flow of

parts and components between countries. Trade barrier reduction in the 1980s accelerated the

growth of world trade, effected the integration of most of the developing countries into the

world economy, and caused a reorganization of the production structure. Productions are

vertically sliced and fragmented across countries with different specializations, resulting in

multiple back-and-forth trades in intermediate goods until a final product is assembled

(Feenstra 1998).

In the presence of foreign value added, gross values of exports and imports are no

longer an appropriate measure of a country’s integration into the world economy. Who

produces for whom in the world economy, to quote Daudin et al. (2011), becomes a puzzle

waiting to be solved. In response to the measurement challenge, literature has been

blossoming ever since the pioneering Hummels et al. (2001) that first defined the meaning of

vertical specialization, which many subsequent empirical works have been adopted and

improved1.

However, the importance of tracing the sources and uses of value added that are

embodied in trade goes beyond the measurement challenge. When countries are tied together

through global production sharing, how does shock propagate across chains of production

and thus countries? In terms of magnitude of the response, does it matter whether a country

lies in the upstream or the downstream of production in the face of supply and demand

shocks? Understanding the macroeconomic interdependence between countries participating

in production sharing is fundamentally critical for other more important macroeconomic

questions such as the design of optimal monetary coordination.

1 According to Hummels et al. (2001), vertical specialization occurs when goods are produced in multiple

sequential production stages involving two or more countries. At least one country must use imported goods in

its chain of processing, and some of the resulting output must be exported either as intermediate or final goods.

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To take up this challenge, this paper blends the recent and actively growing literature

on the measurement of the value added in trade by using the global input-output framework

with the workhorse two-country dynamic New Keynesian model expanded to feature three

sequential processing stages. Questions such as whether a country participates in production

fragmentation or whether a participating country specializes at the upstream, midstream or

downstream stage of the production process are answered endogenously by the data using

Bayesian inference.

Building on the work by Johnson and Noguera (2012a, 2012b), Daudin et al. (2011),

Hummels et al. (2001), and, particularly, Koopman et al. (2010), we decompose the gross

exports, generated by using the Bayesian estimated model, into domestic and foreign value

added that are compatible with the most comprehensive definition of value added in gross

exports available in the empirical literature. In so doing, trade structure of the model becomes

transparent as we know where the value was added and how the value added is used. In

addition, in the spirit of Johnson and Noguera (2012a, 2012b), we identify the extent of

bilateral production fragmentation, and, similar to Koopman et al. (2010), we have

constructed an index that gauges the country upstreamness in production sharing.

Yi (2003) preceded our effort in modeling three production sequences through which

the final output is produced. However, what distinguishes our model from his dynamic

Ricardian trade model with nontradable final goods is that the outputs of all stages in our

model are tradable. This simple innovation is fundamental in quantifying the domestic value

added embodied in the export of intermediates shipped back to the source for downstream

production and in accounting for the foreign value added in the final domestic product

exports. We show that these are two components in value added that are important in

identifying the country’s position in the value chains.

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Next, we use the framework to shed light on international shock transmission. Our

results indicate that whether favorable total factor productivity shock originates from an

upstream or downstream country, it tends to lift up the aggregate value added of countries

tied together by production sharing. In other words, vertical linkage in production has

synchronized the responses of participating countries toward shocks (di Giovanni and

Levchenko, 2010). The responses of an upstream country are magnified when its shock

correlates with the shock originated in a downstream country. This finding corroborates the

recent empirical finding regarding the role of vertical specialization in the great trade collapse

(Bems et al., 2010; Levchenko et al., 2010).

2. A New Keynesian model of production fragmentation: Key ingredients

In this section, we outline a two-country New Keynesian model of production

fragmentation. We added two innovations to the otherwise standard New Keynesian model.

First, final output is processed through three sequential stages. The upstream firms combine

labor services and capital in Cobb-Douglas production technology to produce materials that

are partially exported abroad for subsequent processing, with the remaining materials used

for local midstream remanufacturing in conjunction with the imported intermediate inputs. A

fraction of the remanufactured intermediate goods would then be re-exported for final

assembly in downstream production. The assembled final goods are consumed and invested

locally or exported. Invested final goods constitute the capital inputs for upstream production,

which later become the intermediates for subsequent processing. As such, we have outlined a

model of production fragmentation with “intermediate loops”. Figure 1 provides illustrations

on this production and trade structure.

[INSERT FIGURE 1 HERE]

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Whereas a typical New Keynesian model with two stages of production can only

account for import of intermediates for final assembly and export in sequence, our model

simultaneously embraces the equally important sequential import and export of intermediate

inputs. With this parsimonious model, we can comprehensively trace the cross-border flow of

value added in the spirit of Koopman et al. (2010).

The second innovation is the assumption of trade invoicing in U.S. dollars as most

international trade is conducted in U.S. currency (Goldberg and Tille, 2008). This innovation

contradicts the typical practice in New Open-Economy Macroeconomics that assumes either

producer or local currency pricing.

Given the dollar price of export, depreciation against the U.S. dollar increases unit

export price in local currency. Although nominal depreciation translates into a higher local

price of imported intermediate inputs, the expanding export revenue helps firms absorb the

negative impact of depreciation on markup without the need to proportionally raise the output

price for the home and export market. As a result, the dollar pricing mechanism lies between

a zero exchange rate pass-through in local currency pricing mechanism and a complete

exchange rate pass-through into output price in producer currency pricing mechanism, while

retaining close movement between the nominal exchange rate and the terms of trade.

Below, we elaborate on our discussion of the model.

2.1. Chains of production from upstream to midstream and downstream

A unit mass of competitive firms at upstream production has access to Cobb-Douglas

production technology of (1) that uses plant-specific capital ��, � ∈ �, and a continuum of

differentiated labors � = � �(�)��,��,� ��∈� ��,��,�� to produce plant-specific materials ��

at date t.

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�� = �� !(�)��! (1)

where "� is a first-order autoregressive Hicks-neutral total factor productivity (TFP) shock.

The upstream firms can only alter its capital over time by varying the rate of investment #��

that comes with a cost S�#�� #��$ . Capital stock accumulation evolves according to the form

in Mandelman et al. (2011)

�� = (1 − ')�� + u�� #�(�) )1 − Ψ* +u��, ��(�)u�,��(�) - + .�,��(�).��, ��(�) − Λ-*/ (2)

where u�� is investment-specific technology (IST) shock, and follows first-order

autoregressive process. The parameter Ψ denotes investment adjustment cost, and Λ

determines how forward-looking the investment decision is.

The upstream firm thus optimally chooses the path of ��, �, and #�� to minimize the

cost of production (01,� + ')�� + 2�� subject to output net of investment adjustment cost,

Φ�� )�� !(�)��! − Ψ* u�� #�� 3 .�,��4.��, ��4 − Λ5* = 0/ , where Φ�� is Lagrangian

multiplier which we define as the real marginal cost for upstream firm.

2� = � 2�(�)��,��,� ��∈� ��,��,�� refers to the real wage and 01,� is the real return on capital.

Both correspond to respective marginal productivity. 78,� denotes the wage elasticity of the

demand for labor �. For the sake of simplicity, we assume that the market for upstream goods

is tightly competitive. The elasticity of substitution between varieties is thus close to infinity,

and as a consequence, price approximates real marginal cost. The output are used as

intermediates for either domestic or foreign midstream production, �� ≡ ��:��: + ��:��;. The

marginal product of capital stock and labor, and the intertemporal optimal investment

decision are derived as

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�� = 3 �<=,�5 >Φ�� (3)

� = + �?�- (1 − >)Φ�� (4)

Φ�� 3 .�,��4.��, ��4 − Λ5 = Φ��@� )3.�A�, ��A�4.�,��4 − Λ5 3.�A�, ��A�4

.�,��4 5 − �* 3.�A�, ��A�4.�,��4 − Λ5*/ (5)

Equations (3) and (4) combined with production function (1) give us the real marginal cost of

upstream firm.

Φ�� = +<=,�4 @B-C(?�)��CDE�!C(��!)��C (6)

A mass continuum of midstream monopolistically competitive firm �, � ∈ �, imports

c.i.f upstream goods F�;,��: of plant � for remanufacture in combination with local inputs ��:,��:

using CES production technology as in equation (7)

�*�� = �(1 − G*)�H��:,��: H��H + (G*)�H�F�;,��: H��H � HH�� (7)

whereF�;,��: = 3 F�;,��: (�)�I��I� ��∈J 5 �I��I�� and ��:,��: = 3 ��:,��: (�)�I��I� ��∈J 5 �I��I��

. The optimal

demand function for the � varieties of F�;,��: (�) is �L�;,�� (�) L�;,��$ �MI�F�;,��:, and of ��:,��: (�) is

�L�:,�� (�) L�:,��$ �MI��:,��:. L�:,��

and L�;,�� are the domestic price of local and imported

materials, respectively. 7*� > 1 is the time-varying demand elasticity. The parameter G*

indicates the share of imported intermediates in midstream production, and the parameter

O > 0 denotes the elasticity of substitution between home and imported intermediate inputs.

Midstream firm � minimizes the cost function L�:,�� :,��: + L�;,�� F�;,��: subject to

Φ*�� P�*�� − �(1 − G*)�H��;,��: H��H + G* �H�F�;,��: H��H � HH��Q, where Φ*�� is real marginal cost of

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midstream firm to obtain the following optimal demand schedules for domestic and foreign

inputs

��:,�� = (1 − G*) RS�T,�4S�,�4 U�V �*�� (8)

F�;,��: = G* RS�W,�4S�,�4 U�V �*�� (9)

By substituting the first-order condition for ��:,��: and F�;,��:

, we can obtain the real marginal

cost for midstream firm.

Φ*�� = L�� = X(1 − G*)�L�:,�� V + G*�L�;,�� VY ��H (10)

Note thatL�� is the flexible production-based producer price for midstream production. The

market is cleared by the demand from home and foreign downstream firm, �*�� ≡ �*:,��: + �*:,��;.

Lastly at downstream production, a continuum of monopolistically competitive final-

good producers � of measure � combines a variety of home �*:,��: and imported intermediate

goods F*;,��:using the following CES technology to produce consumer goods.

�Z�� = �(1 − GZ)�H��*:,��: H��H + GZ �H�F*;,��: H��H � HH�� (11)

where �*:,��: = + �*:,��: (�)(M[��) M[�⁄ ��∈J - �[��[�� and F*;,��: = + F*;,��: (�)(M[��) M[�⁄ ��∈J - �[��[��

.

The demand schedules for � varieties of domestic and imported intermediates take the form

�*:,��: (�) = �L*:,�� (�) L*:,��$ �M[��*:,��: and F*;,��: (�) = �L*;,�� (�) L*;,��$ �M[�F*;,��:

.The parameter

GZ denotes the share of imported intermediate inputs in final-good production. Subject to

Φ3^� P�Z�� − �(1 − GZ)�H��*:,��: H��H + GZ �H�F*;,��: H��H � HH��Q, where ΦZ�� is real marginal cost of

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downstream firm, likewise, downstream firm � minimizes the cost function L*:,�� *:,��: +L*;,�� F*;,��:

to yield the following optimal demand for domestic and imported intermediates.

�*:,�� = (1 − GZ) RSIT,�4SI,�4 U�V �Z�� (12)

F*;,��: = GZ RSIW,�4SI,�4 U�V �Z�� (13)

The real marginal cost for downstream firm is derived as

ΦZ�� = L*�� = X(1 − GZ)�L*:,�� V + GZ�L*;,�� VY ��H (14)

L*�� is staggered producer price index for downstream firms. The final output is partly

consumed by domestic and foreign consumers with the remaining invested as capital stock to

produce upstream goods, �Z,�� ≡ _:,��: + �Z:,��; + #��.

2.2. Transportation cost

Following Ravn and Mazzenga (2004), we measure transportation cost as the wedge

between c.i.f. value of import and the corresponding f.o.b. value of export in such a way that

1 + `� = a�W,�4Tb�W,�4T = aIW,�4T

bIW,�4T = cW,�dTb[W,�4T (15)

2.3. Optimal pricing decision with U.S dollar pricing in trade

Pricing decision is assumed to be time dependent. The ability of domestic firms at

midstream and downstream production to re-optimize the price is subject to the signal

received at probability 1 − eSf, for g = 2,3. Firm � that receives the signal chooses ℙf:,� to

maximize the following expected discounted profits j�Π� for sales in home market

j�Π�:klD = j� ∑ (eSfn)�Λ�@� �ℙoT,�Ad4 �aco,�AdSo,�Ad � �ℙoT,�Ad4

SoT,�Ad��Mo,� �f:,�@��:∞�pq (16)

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Contrary to producer-currency pricing decision in the typical New Keynesian model,

or local-currency pricing in the New Open-Economy model, we consider U.S. dollar pricing

strategy in exports. This assumption is apparently coherent with the fact that international

trade is largely denominated in the U.S dollar. The variability of exchange rates between

local currency and the U.S. dollar r:s,� will not pass through into foreign price of home

export, but rather, it will pass through into local-currency denominated export earnings. Firm

� signaled for price reoptimization chooses ℙf:,�s to maximize the expected export profit in

home currency

j�Π�tS = j� ∑ (eSf∗ n)�Λ�@� vwTx,�ℙoT,�Adx (�)�aco,�AdSo,�Ad y �wWx,�ℙoT,�Adx (�)

SoT,�AdW ��Mo,� �f:,�@��;∞�pq (17)

In what follows we assume that all firms are symmetric in price setting.

Firms allowed for price re-optimization will reset their log-linearized price ℙzf:,�fD{ to

approximate the optimal reset price derived from expected discounted profits (16) and (17),

respectively, for home and export market. The remaining firms that do not receive signal for

re-optimization will stick to last-period price, out of which a fraction of them |Sf will index

to last-period inflation. Probability-weighted inflation dynamics of producer price (}*:,�),

GDP deflator (}Z:,�), intermediate export price (}*:,�s ) and final export prices (}Z:,�s ) can be

derived as

}f:,� = + ~�o�@��o�~�o- }f:,�� + + ��@��o�~�o- j�}f:,�@� + ��Φz f,� + �f,� (18)

}f:,�s = 3 ~�ox�@��ox �~�ox 5 }f:,��s + 3 ��@��ox �~�ox 5 j�}f:,�@�s + �s�Φzf,� − �:s,� + �f,�s (19)

where � = (��o)(��o�)��o(�@��o�~�o) and �s = ��ox ��ox � ��ox ��@��ox �~�ox . �f,� is an i.i.d price markup shock for

g = 2,3. Φzf,� is the log-deviation of real marginal cost, in which Φz*,� = ��,� and ΦzZ,� = �*,�.

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2.4. Household

Consider a continuum of infinitely-lived households, represented and indexed by

i∈ �0,1�, who possess the utility function of

� = j� �∑ n�u�c v(c�d��)�� − u�8 (8�d)�A�

�@� y∞�pq � (20)

where

_�� = v(|)��_:,��: �� + (1 − |)��_;,��: �� y ��

(21)

u�c and u�8 , respectively, arei.i.d preference and labor supply shock.

_:,��: �= 3 _:,��: (�)�� ∈� 5 ��and_;,��: �= 3 _;,��: (�)�� ∈� 5 �� are the composite varieties

of home and imported consumer goods. ��(= �_�� ) indicates external habit formation in

which b is the parameter that governs the extent of habit persistence. 0 < n < 1 refers to

subjective discount factor, � measures the coefficient of relative risk aversion, and the

reciprocal of �indicates the wage elasticity of labor supply. The parameter � > 1 denotes the

elasticity of substitution between home and imported consumer goods. The parameter

| measures home bias. Household i’s constrained optimization problem can be illustrated as

maximization of utility function (20) subject to consumption basket (21) and the following

flow budget constraint

_� + +wTx,�S��- 3 ��W��5 + ��S�� + �� = 2� � + Π� + 01,�� + 3wTx,��W @��S� 5 (22)

where L:,� and L;,� , respectively, denotes domestic price of home and imported consumer

goods. Household facing exchange-rate risk � in foreign asset market has access only to

imperfect international asset market. Note that foreign bond ¡�; is denominated in U.S. dollar.

Thus, the nominal exchange rate between home currency and the U.S. dollar is considered.

Solving for the utility maximization problem gives us the marginal rate of substitution

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between works and consumption (23), intertemporal substitution of consumption (24), and

uncovered interest rate parity (25).

�� _�� − �_�� u�8 = 2�a�w (23)

�c�d�¢c��d ��S� u�c = n(1 + 0�) �£�c�A�d �¢c�d ��

£�S�A� j�u�@�c (24)

r:s,� = j�r:s,�@� +�@<��@<� - � (25)

L� += ¤|L:,��¥ + (1 − |)L;,��¥¦� (��¥)⁄ - is the utility-based consumer price index (CPI).

Since household is a monopoly supplier of differentiated services, nominal wage is set

in Calvo-style, which results in nominal wage inflation dynamics as what follows:

}�{ = § ~¨�@�¨�~¨© }��{ + § ��@�¨�~¨© j�}�@�{ + �{(ª«�a�w − ª«� + u�{) (26)

where �{ = (��¨)(��¨�)�¨(�@�¨�~¨) . The parameter e{ denotes wage stickiness, and |{ is wage

indexation. u�? is i.i.d wage markup shock. Note that nominal wage inflation responds

positively to the wedge between wages demanded by optimizing household and marginal

product of labor.

2.5. Trade balance, aggregate value added, and monetary policy

We define trade balance as the balance between aggregate f.o.b exports and aggregate

c.i.f imports.

¬� = ��:,��; + �*:,��;�∈J �� + �Z:,��;�∈J �� − F�;,�: − F*;,��:�∈J �� − _;,��:�∈� �� (27)

The aggregate value added of the economy (), which corresponds to gross domestic product

in data,can be defined as

� = _� + #� + ¬� (28)

The model is lastly closed by considering a general form of monetary policy reaction as

below:

0� = ®�0�� + (1 − ®�)�0�f + °}cS�,� + z� + ∆w∆�:s,� + u�� (29)

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where0�f+= u�c + �(²�� + ³�)- is the natural rate of interest influenced by the efficient shocks,

®� measures the interest rate persistence, °, , and ∆w , respectively, indicates central

bank’s responsiveness toward variability in CPI inflation, aggregate demand variability, and

rate of change in nominal exchange rates between home currency and U.S. dollar. u��refers to

i.i.d white noise to the conduct of monetary policy.

3. A Bayesian Measurement

The model is estimated using the Bayesian method. Bayesian estimation is principally

about identifying a set of parameters that maximize the posteriors µ(¶|¸, ℳ) as a product of

the likelihood function of data derived from the model µ(¸|¶, ℳ) using the Kalman filter

and the prior probability distribution of the parameters µ(¶, ℳ):

µ(¶|¸, ℳ) = µ(¸|¶,ℳ)µ(¶,ℳ) µ(¸|¶,ℳ)µ(¶,ℳ)s¶¶ (30)

where ¶ is a vector of model parameters, and ¸(= ℝ�, … , ℝ¼) is a set of observed data over

½ number of periods (see, for instance, Fernandez-Villaverde, 2010 for detailed discussion).

3.1. Data

In addition to China, we study nine East and Southeast Asian economies including

Japan, the Republic of Korea, Hong Kong, Taiwan, Singapore, Malaysia, Thailand, Indonesia,

and the Philippines. The country selection is motivated by the fact that these Asian

economies are vertically specialized in trade. Whereas production sharing is equally observed

in the rest of the world, the depth and complexity of production fragmentation and trade in

East Asia is unparalleled. In a study of 79 countries and over 121 categories of goods from

1967-2005, Amador and Cabral (2009) show that out of the top ten vertically specialized

countries, eight are located in East Asia (see, also, Sawyer et al., 2010). Furthermore,

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Koopman et al. (2010) argue that the positions of advanced and emerging Asian countries in

the global production chain of the manufacturing sector are diverse with Japan occupying the

most upstream production, Korea and Taiwan in midstream production, and China in the

most downstream production. These factors make Asian economies an ideal sample for our

investigation.

We analyze the quarterly time series from 2001 to 2008 due to the fact that the

addition of China to the World Trade Organization at the end of 2001 fundamentally changed

regional production sharing by substituting Southeast Asia as the destination for final

assembly of intermediates into consumer goods exported to the United States, Europe, and

the rest of the world (see, for instance, Kim et al. 2011, and Athukorala, 2009). Excluding

China (CN), we categorize Indonesia, Malaysia, Philippines, Thailand as developing

Southeast Asian economies (SEA4) and Japan, the Republic of Korea, Hong Kong, Taiwan,

and Singapore, as advanced East Asian economies (EA5). Thus, there are three two-country

models to be estimated: the SEA4-EA5 model, the CN-EA5 model, and the CN-SEA4 model.

The name that appears first is treated as home country and the name that appears second is

treated as a foreign country.

There are nineteen macroeconomic observable variables used in estimation, including

GDP; consumption; investment; labor force; nominal short-term interest rate; nominal

exchange rates between home currency and the U.S. dollar; PPI inflation; GDP deflator

inflation; CPI inflation for SEA4, EA5, and China in a two-country setting; and the U.S.

federal funds rate. All the quantity variables are deflated by the respective deflators, and all

data, except for the rates of inflation and interest, are logged and de-trended using the

Hodrik-Prescott filter with a smoothing parameter of � = 1600. We then construct a cyclical

observable series for SEA4 and EA5 weighted by the time-varying fraction of national total

trade over aggregate regional trades.

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3.2. Priors and posteriors

Table 1 reports the priors and probability distribution functions. We assume symmetric

priors for both home and foreign country. Nonetheless, we allow different posteriors for price

indexation and stickiness, the share of imported intermediate inputs, home bias in

consumption, monetary policy reaction functions, and standard deviation of structural shocks.

We use Dynare 4.3 algorithms for model estimation and adjust the number of Markov chains

to ensure that estimates for mean and standard deviation within and across Markov chains are

consistent.

In addition, we have assumed a uniform distribution for priors where the true value is

uncertain because of the lack of previous Bayesian studies on this region. The priors include

the share of imported inputs at midstream and downstream production, price stickiness, and

the standard deviation of shocks. Thus, equal probability is assigned for all potential

parameter values within a theoretically coherent range. The priors for efficient shock

persistence are in beta distribution, while the parameters in monetary policy reaction function,

which theoretically must have positive values, are in gamma distribution with prior means

following the standard assumption.

[INSERT TABLE 1 HERE]

Table 2 reports the estimates of mode, mean and probability interval for selected

parameters in the SEA4-EA5 model, the CN-EA5 model, and the CN-SEA4 model. All

structural shocks and parameters are nicely identified, as evidenced by the proximity between

posterior mode and mean, which falls within the 90% probability interval. Two intermediate

input parameter estimates are particularly worthy of greater discussion. First, Table 2 shows

that China, Southeast Asia, and East Asia are tightly bound in the sense that midstream and

downstream productions in these economies heavily use each other’s export of intermediate

inputs.

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Second, the estimated elasticity of substitution between domestic and imported

intermediates is greater than one, irrespective of models. This finding is in interesting

contrast to the existing empirical finding of inelastic substitution because of the

complementarities between domestic and foreign inputs (see, for instance, Luong, 2011).

However, such empirical estimates are about the elasticity of substitution between

intermediate inputs across different final outputs, whereas elasticity of substitution between

intermediates is within a final output sector in our context. More importantly, di Giovanni

and Levchenko (2010) argued that the elasticity of substitution is not as empirically important

in the bilateral business cycle comovement as the literature on trade-comovement puzzle has

theoretically speculated (see, for instance, Kose and Yi, 2006).


4. Tracing value added, production fragmentation, and country upstreamness

Koopman et al. (2010) offer the most detailed definition of vertical specialization to

date by breaking down gross exports into the foreign value added in domestic exports of

intermediates and final goods – the earliest definition of vertical specialization by Hummels

et al. (2001) – and the domestic value added embodied in the exports of the following:

(1) final goods and services absorbed by the direct importer;

(2) intermediates used by the direct importer to produce its domestically required

products;

(3) intermediates used by the direct importer to produce goods for third countries; and

(4) intermediates used by the direct importer to produce goods shipped back to source.

4.1. Decomposing the value added of gross exports

We contribute to this literature by deriving an equation from the estimated model that

corresponds exactly in definition to the Koopman et al. (2010) decomposition. This exercise

is useful in two mutually beneficial ways. First, it provides a macroeconomic perspective of

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vertical specialization that corresponds to the micro evidence, paving the way for the

computation of upstreamness of countries engaged in global production sharing vis-à-vis

trading partner. Second, the use of the international business cycle model to explain the

macroeconomic implications of vertical specialization is more transparent because of its

ability to account for the different types of value added in trade.

To be compatible with the decomposition of Koopman et al. (2010), we break down

gross exports to domestic value added embodied in exports ¿¯", “reflected domestic value

added” ¯r1 ∗, and the foreign value added used in exports, ¯r:

À� = Á ¿¯"f,�f + ¯r1 ∗�+ ¯r�

where

∑ ¿¯"f,�f =)1 − aIW,�T

b[� R1 − a�T,�WbI�W U/ �Z:,�;ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(�)ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ�

+ 31 − aÆW,�Tb�� 5 Ra�T,�W

bI�W U �*;,�;ÂÃÃÃÃÃÃÄÃÃÃÃÃÃÅ(��)+ 31 − a�W,�T

bI� 5 RaIT,�Wb[�W U �_;,�; + #�; ÂÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÅ(��)ÂÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÅ*

(31)

¯r1 ∗�= 31 − aÆW,�Tb�� 5 Ra�T,�W

bI�W U �*;,�:ÂÃÃÃÃÃÃÄÃÃÃÃÃÃÅ(�Ç)+ 31 − a�W,�T

bI� 5 RaIT,�Wb[�W U �Z;,�:ÂÃÃÃÃÃÃÄÃÃÃÃÃÃÅ(Ç)ÂÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÅÈ

(32)

¯r� = R1 − aÆT,�Wb��W U 3a�W,�T

bI� 5 �*:,�;ÂÃÃÃÃÃÃÄÃÃÃÃÃÃÅ(Ç�)+ R1 − a�T,�W

bI�W U 3aIW,�Tb[� 5 �Z:,�;ÂÃÃÃÃÃÃÄÃÃÃÃÃÃÅ(Ç��)

(33)

By adding and simplifying equations (31) to (33) together with the transportation cost, we

obtain the standard definition of gross exports, À� ≡ ∑ �f:,�;Zfp� . Thus, it verifies our

decomposition.

Component (1) in equation (31) represents the domestic value added from the export

of final goods and is calculated using the residuals between final output and the imported

intermediates in gross output. Because imported intermediates F*;,�: comprise domestic value

18

added embodied in an earlier stage of foreign production, we add F�:,�; as a share of gross

foreign midstream output back into component (1). Component (2) in equation (31) refers to

the domestic value added embodied in the export of domestic intermediates for foreign local

needs at midstream F�:,�; (item (ii)) and downstream level F*:,�;

(item (iii)) as a share of

gross foreign output, respectively. Domestic intermediate production contains foreign value

added because foreign intermediates from an earlier stage were used. This value must be

removed. However, Fq;,�: = 0 because upstream production only uses domestically owned

inputs.

In contrast to component (2), component (4) in equation (32) indicates domestic value

added embodied in the domestic intermediates used in foreign production for re-exporting

back to the source as intermediates (item (iv)) or final goods (item (v)). Likewise, foreign

value added incorporated at an earlier stage of production of domestic intermediates must be

taken into account. Finally, equation (33) informs us about the foreign content of domestic

exports, after accounting for the domestic value added embodied in foreign intermediates.

Consider the definition of the log-linearized variable: É� = ÊËÌ +Í�ÍÎ -, where ÏÎ refers to

the steady-state value. It implies that Ï� = ÏÎ� Ð�. By considering the relationship between c.i.f

import and f.o.b export, as in equation (15), our decomposition of gross export can be

rewritten and rearranged for measurement as follows:

1 = )1 − GZ R1 − ÑI��@ÒÎW DÓ�WU/ 3ÔÎ[TW

ÀÕ 5 �+Ô[T,�W �À«�-ÂÃÃÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÃÃÅ(�)+ ) ÑIW��@ÒÎW DÓ�W/ RÔÎIWW

ÀÕ U �+ÔIW,�W �À«�-ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(��)+

(1 − G*) ) Ñ[W��@ÒÎW DÓ�W/ )RÖWWÀÕ U �+ÖW,�W �À«�- − +ØWÀÕ - �+Ø�W�À«�-/ÂÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÃÃÃÃÃÅ(��)

+ ) ÑIW��@ÒÎW DÓ�W/ 3ÔÎIWTÀÕ 5 �+ÔIW,�T �À«�-ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(�Ç)

+

19

(1 − G*) ) Ñ[W��@ÒÎW DÓ�W/ 3ÔÎ[WTÀÕ 5 �+Ô[W,�T �À«�-ÂÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÅ(Ç)

+ G* 3ÔÎITWÀÕ 5 �+ÔIT,�W �À«�-ÂÃÃÃÃÃÄÃÃÃÃÃÅ(Ç�)

+

)1 − ÑIW��@ÒÎW DÓ�W/ GZ 3ÔÎ[TWÀÕ 5 �+Ô[T,�W �À«�-ÂÃÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÃÅ(Ç��)

(34)

where Gf ≡ Ff��,;,�: �f,�$ .

4.2. Relation to existing models and measurements

How important is it to set three sequential stages of production where outputs of all of

the chains can be traded? To answer this question, we consider three different dominant

models of international business cycles with trade: the international real business cycle model

of Raffo (2008), the open-economy New Keynesian model of Smets and Wouters (2003), and

the dynamic Ricardian trade model of Yi (2003).

Raffo (2008) considers two-stage productions where domestic intermediates cross

international borders for foreign final production, and vice versa, while final goods are non-

traded. Smets and Wouters (2003) also employ a two-stage production structure but allow

both intermediates and final goods to be traded. Yi (2003) resembles our model the most, in

that the final good is produced in three sequential stages. The notable difference is that final

goods are not tradable in Yi (2003), although both upstream and midstream outputs are. By

matching equations (31) to (33) to the trade structure of each of the aforementioned models,

the value-added decomposition of gross exports in these models can be written as:

International RBC of Raffo (2008): À� = 31 − a�W,�TbI� 5 RaIT,�W

b[�W U �_;,�; + #�; ÂÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÅ(��)

NK model of Smets and Wouters (2003):

20

À� = �1 − F*;,�:�Z� Ù1 − F�:,�;

�*�; Ú� �Z:,�;ÂÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÅ(�)+ R1 − F�;,�:

�*� U ÙF*:,�;�Z�; Ú �_;,�; + #�; ÂÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÅ(��)

+ R1 − F�;,�:�*� U ÙF*:,�;

�Z�; Ú �Z;,�:ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(Ç)+ Ù1 − F�:,�;

�*�; Ú RF*;,�:�Z� U �Z:,�;ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(Ç��)

Dynamic Ricardian trade model of Yi (2003):

À� = R1 − Fq;,�:�� U ÙF�:,�;

�*�; Ú �*;,�;ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(��)+ R1 − F�;,�:

�*� U ÙF*:,�;�Z�; Ú �_;,�; + #�; ÂÃÃÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÃÃÅ(��)

+ R1 − Fq;,�:�� U ÙF�:,�;

�*�; Ú �*;,�:ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(�Ç)+ Ù1 − Fq:,�;

��; Ú RF�;,�:�*� U �*:,�;ÂÃÃÃÃÃÃÃÄÃÃÃÃÃÃÃÅ(Ç�)

Many important genres of value added in domestic and foreign trade have been left out

of these models. The case of Raffo (2008) supported the argument of Hummels et al. (2001)

that vertical specialization is more than trade in intermediate goods. Vertical specialization

involves exports and imports. Beside, as shown in Table 3, the missing domestic value added

in intermediates exported back to the source in Smets and Wouters (2003) and the foreign

value added in domestic exports Yi (2003) are too critical to be ignored when measuring the

country upstreamness in production sharing.

Constrained by a two-country setting, our model is unable to account for the domestic

value added embodied in the export of intermediates that will be re-exported to a third

country by a direct importer after processing. Even so, relative to the existing models, our

model permits the most comprehensive break down by matching the Koopman et al. (2010)

decompositions so that, divided by the gross export, ∑ ¿¯"f,�f is the VAX ratio of Johnson

and Noguera (2012a, 2012b); ¯r1 ∗� corresponds partly to VS1 by Hummels et al. (2001)

and exactly to VS1* in Daudin et al. (2011); and ¯r� matches the Hummels et al. (2001) ¯r

definition.

21

4.3. Identifying production fragmentation and the upstreamness of countries

Based on the estimated Gf , the calibrated “great ratios” for the market-clearing

condition of each stage, the steady-state transportation cost, and the data generated from the

estimated model, Table 3 provides a numerical simulation of the models.


Looking first at bilateral vertical specialization in gross exports (VS), the estimates

range on average from 20.11% to 34.97% during the period from 2001Q1 to 2008Q4.

Although not exactly comparable, this measure is aligned with the estimates of multilateral

vertical specialization of gross export obtained by Koopman et al. (2010) that range from

23.65% for EA5 (excluding Singapore), to 32.28% for SEA4 and to 33.8% for China in 2004

for the manufacturing sector. In addition, the measures are comparable to those obtained in

Amador and Cabral (2009) that, as a share of gross import, range from 20.3% for China to

24.5% for EA5 (excluding Japan) and to 28.9% for SEA4 (excluding Indonesia) during the

period from 2001-2005.

The VS ratio is imprecise as a measure of production fragmentation. For example,

suppose Country A produces only at the downstream stage for final goods export with

intermediates imported entirely from abroad. By contrast, Country B slices up both the

midstream and downstream production with approximately half of the intermediates imported.

The vertical specialization as a share of gross exports for Country A is equivalent to Country

B despite the fact that the latter has more fragmented production chains. The VAX ratio

proposed by Johnson and Noguera (2012a, 2012b) is more intuitively straightforward as a

measure of production fragmentation.

If the exports do not contain imported intermediates, which implies the absence of

production fragmentation, then the VAX ratio will be 100%. In other words, as Johnson and

Noguera (2012b) argued, the ratio declines when foreign intermediates are used in the final

22

goods export to the direct importer ((i) in Table 3) and when exported intermediates are used

for local needs ((ii) and (iii)). Back-and-forth trade in intermediates, made possible by

production fragmentation, also multiplies gross exports more proportionally than value added,

depressing the ratio further.

That said, by using the bilateral VAX ratio, Table 3 clearly shows that production in

advanced East Asian economies has been on average more vertically fragmented than in

Southeast Asian economies (22.85% versus 72.54%) and China (25% versus 59.13%). In the

case of China and Southeast Asia, China is slightly ahead of Southeast Asia (43.08% versus

52.29%).

Decomposing gross exports into domestic and foreign value added facilitates the

construction of an index that helps us to trace the upstreamness of a country within the global

production sharing chain. Intuitively, for countries engaged upstream of the production

sharing, intermediate exports used by a foreign importer are more likely to be shipped back

home for further processing. As a result, reflected domestic value added in the gross exports

of upstream countries will be more than proportionate to the foreign value added in its gross

exports.

Thus, in the spirit of Koopman et al. (2010), we propose an upstreamness index

computed as the home country’s log ratio of ¯r1 ∗ to ¯r in gross exports.

� = Êg +1 + Ûw�∗À� - − Êg +1 + ÛwÀ� - (35)

Not surprisingly, Table 3 shows that East Asian economies with an index of more than one

stay at the upper end of the production chain compared to Southeast Asia and China. This

largely confirms the findings of Kim et al. (2011), Koopman et al. (2010) and Athukorala

(2009): Japan lies upstream in the production chain by providing intermediate inputs and

China lies downstream in the production chain by using imported intermediate inputs to

23

provide final goods to the world, while other Asian economies, including Hong Kong, Korea,

Taiwan, Malaysia, and Philippines, lie in between.

What makes our story interesting is that both China and Southeast Asia lie

downstream in their bilateral interaction. This suggests that while China complements

advanced East Asian economies as an absorber of the latter’s capital and intermediate goods,

China competes head-to-head with Southeast Asia at the final goods market (see, for instance,

Haltmaier et al., 2007 and Eichengreen et al., 2007).

5. Does country upstreamness matter for international shock transmission?

When foreign intermediates are heavily used and productions are highly fragmented

and linked, as Table 3 has shown, one expects greater synchronization in the business cycles

of these economies. In fact, di Giovanni and Lechvenko (2010) found that vertical trade is too

important of a determinant to bilateral business cycle comovement to be ignored. He and

Liao (2012), Moneta and Ruffer (2009), and Shin and Wang (2003), to name few, have found

increasingly synchronized business cycles in Asia made possible by intra-industry trade.

Figure 2 vividly illustrates this point by comparing bilateral cross-correlation of simulated

data with the actual series across three estimated models. During the period of 2001 to 2008,

these economies comove tightly wherein most bilateral exports and imports are synchronized

contemporaneously, followed by gross domestic product and consumption. And our

estimated model of production fragmentation and vertical trade is able to replicate the

business cycle comovement, although not perfectly.


Business cycle synchronization, made possible by trade integration, is often viewed as

the underlying condition for the formation of a monetary union. However, business cycle

synchronization does not necessarily imply symmetric responses toward macroeconomic

24

shocks. While the business cycles of two countries that are heavily vertically linked in

production and trade comove over a period in response to a variety of shocks, they may

respond asymmetrically towards an identical shock. In fact, the seminal Bayoumi and

Eichengreen (1994) have long noted that “output comovements are not the same as shocks.”

Even studies attempting to distinguish common from country-specific shocks confuse

disturbances and responses. We believe that more light needs to be shed on the latter in the

discussion of macroeconomic interdependence.

5.1. Supply shock

Consider a 1% increase in the innovation of total factor productivity (TFP). We assess

the dynamic response of the aggregate value added (GDP) of each region towards both

common – if home and foreign TFP shock are perfectly correlated – and regional-specific

TFP shock, as shown in Figure 3. Vertical reading of the region indicates the place where

shock originates, whereas horizontal reading refers to the responses. As far as idiosyncratic

shock is concerned, China’s favorable TFP shock marginally increases the GDP of the East

Asian countries engaged in upstream production, but not of Southeast Asia, which is involved

downstream in bilateral production fragmentation.


By contrast, positive shocks to downstream Southeast Asian TFP that expand GDP

help downstream China’s GDP to marginally prosper; however, it does not affect upstream

East Asian economies. It is puzzling that favorable shock to upstream East Asian TFP

expands Chinese GDP but not Southeast Asian GDP, even though both are positioned

downstream from East Asia in the production sharing chain. This pattern is robust even when

the TFP shocks to China and Southeast Asia are perfectly correlated with the East Asian TFP

shock. It should be noted that when the TFP shock originates in downstream China, where

the other countries are perfectly correlated, the effect is benign to all regardless of their

25

position in the production sharing chain. What is puzzling is that this is not the case when the

TFP shock originates in downstream Southeast Asia.

Therefore, based on the case of China-East Asia, we can cautiously infer that when an

efficient supply shock strikes, the responses of the countries positioned at different stages of

production that complement one another tend to be synchronized. Nonetheless, for countries

engaged in the downstream production phase, expansion may (or may not) negatively affect

production partner countries.

5.2. Demand shock

However, when facing a demand shock, responses are identical, regardless of the

position in the production sharing chain. Figure 4 illustrates the dynamic response of GDP

when there is a 1% negative shock to the innovation of preference. As a consequence, GDP

of all regions declines. Nevertheless, production upstreamness leaves a mark on the pattern of

responses. When shocks originate in downstream China or Southeast Asia, to which the East

Asian preference shock is correlated, the response of upstream East Asia becomes larger. By

contrast, if the shock originates in the upstream East Asian preference, the responses of

downstream China and Southeast Asia are larger only if the shock is idiosyncratic. For

countries that stay equally in the downstream, the pattern of response is not conclusive. In

particular, Chinese GDP falls more if the shock to the Southeast Asian preference is

idiosyncratic. Quite the opposite, the magnitude of contraction of Southeast Asian GDP is

stronger if the shock to the Chinese preference is correlated with its own.


5.3. Relation to the empirical literature on the great trade collapse and vertical

specialization

Our results indicate that the role of vertical specialization and production upstreamness

in shock propagation, especially in the case of East Asia and China when facing a negative

26

preference shock, corroborates the existing findings on vertical specialization and the recent

great trade collapse. For instance, Levchenko et al. (2010) illustrated that downstream

vertical linkages play a role in the reduction of international trade, which, in turn, contributes

to the collapse of world aggregate value added. In particular, goods that are intensively used

as intermediates for other countries experienced larger percentage drops in imports and

exports. Framed in our context, in the face of negative demand shock the upstream countries

tend to be affected more severely than the downstream countries.

Bems et al. (2010) maintained that both intermediate and final exports from Japan fall

more than exports from China, despite the fact that the United States is a larger direct

importer for China than Japan. Put in our context, the ripples of negative demand shock that

originated in an extra-regional country must first arrive at downstream China and, to some

extent, upstream East Asia, which also exports final goods in production sharing. “Third-

country shock” is akin to common shock in our model with its origins in China. The pattern

of responses of the GDP of China and East Asia towards negative demand shock shown in

Figure 4 fits with this evidence.

The intuition is straightforward. Common shock hits East Asia harder2

because

upstream East Asia is more intensely involved in production sharing with multiple back-and-

forth import and export of intermediates. This is evidenced by higher domestic value added

embodied in intermediates exported back to East Asia for further processing at the midstream

level vis-à-vis China (30.73% versus 7.86%) and Southeast Asia (39.05% versus 0.37%) in

Table 4.

2 Wang and Whalley (2010) document the export performance of Japan, the Republic of Korea, Taiwan,

Indonesia, Malaysia, Thailand, and China over the periods from May 2008 to December 2009, with which our

story depicted in Figure 3 under common shock is compatible. For instance, in the case of the United State as

direct importer, on simple average, month-to-month export performance of the advanced East Asian economies

deteriorates the most by 20.98%, followed by the developing Southeast Asia at 12.64% and China at 3.7%.

27

6. Conclusion

This paper adds to the literature on the measurement of production fragmentation and

value added in trade. However, contrary to the admirably microscopic approach in empirical

research, this paper takes up the challenge through a Bayesian estimated New Keynesian

model expanded to feature three sequential production stages. Outputs of all stages are

tradable. The estimated gross exports from this expanded New Keynesian model can then be

broken down into domestic and foreign value added that are compatible with the most

comprehensive classifications of value added in trade available in the empirical literature.

The usefulness of this macroeconomic approach is twofold. One the one hand, it makes

a model that attempts to explain the macroeconomic implications of vertical specialization

transparent in terms of its ability to account for the types of value added in trade; therefore, it

provides a yardstick on the empirical relevance of the model. On the other hand, it is easier to

proceed to a follow-up investigation on the macroeconomic implications of vertical

specialization in a theoretically and empirically coherent manner. For instance, we find that

the responses of countries bound but positioned at different stages in production sharing tend

to be synchronized even in the face of a country-specific supply shock. In addition, the

magnitude of the response towards common and country-specific shocks is shaped by the

country upstreamness. Upstream countries tend to be more responsive when the shock is

common and originates in downstream countries.

A limitation of the two-country model is its inability to account for the domestic value

added embodied in the export of intermediates that will be re-exported to a third country by a

direct importer after processing. The role of the third country can be important in the trade

dynamics of production sharing. The United States and Europe, for instance, are heavyweight

extra-regional trading partners for East Asia. Setting up and estimating a multi-country model

shall be the venue for the next pursuit.

28

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30

Table 1 The priors for parameters and shocks

Prior distribution

Probability

distribution

function

Mean Standard

deviation

Parameters

Risk aversion coefficient � Uniform 1 0.577

Reciprocal of wage elasticity of labor supply �8 Gamma 2 1.000

Habit persistence � Beta 0.7 0.100

Forward looking-ness of investment decision Λ Uniform 0.5 0.289

Els btw. home and imported intermediate goods O Normal 1.5 0.500

Home bias in consumption | Beta 0.7 0.100

Share of imported materials at intermediate production G* Uniform 0.5 0.289

Share of imported intermediate goods at final production GZ Uniform 0.5 0.289

Employment indexation |{ Uniform 0.5 0.289

Producer price indexation |Ü* Uniform 0.5 0.289

Final goods price indexation |ÜZ Uniform 0.5 0.289

Intermediate export price indexation |Ü*∗ Uniform 0.5 0.289

Final goods export price indexation |ÜZ∗ Uniform 0.5 0.289

Employment stickiness eD Uniform 0.75 0.144

Producer price stickiness eÜ* Uniform 0.75 0.144

Final goods price stickiness eÜZ Uniform 0.75 0.144

Intermediate export price stickiness eÜ*∗ Uniform 0.75 0.144

Final export price stickiness eÜZ∗ Uniform 0.75 0.144

Policy inertia ®� Beta 0.7 0.100

Policy response to inflation ° Gamma 1.5 1.000

Policy response to GDP fluctuation Gamma 0.125 0.050

Policy response to exchange rate variability ∆w Gamma 0.5 0.100

TFP shock persistence ®Ý Beta 0.8 0.100

IST shock persistence ®� Beta 0.7 0.100

Shocks

Total factor productivity �Ý Uniform 0.5 0.289

Investment-specific technology �� Uniform 0.5 0.289

Labor supply �f Uniform 0.5 0.289

Preference �Ö Uniform 0.5 0.289

Producer price markup �°IT Uniform 0.5 0.289

Final goods price markup �°[T Uniform 0.5 0.289

Intermediate export price markup �°IT∗ Uniform 0.5 0.289

Final export price markup �°[T∗ Uniform 0.5 0.289

Transportation cost �Ò Uniform 0.5 0.289

Monetary policy �< Uniform 0.5 0.289

UIPC �Þ Uniform 0.5 0.289

U.S monetary policy �;;< Uniform 0.5 0.289

31

Table 2 Selected posterior distributions for the estimated two-region models, 2001Q1-2008Q4

Southeast Asia (SEA4) East Asia (EA5)

Mode 5% Mean 95% Mode 5% Mean 95%

Parameters

� 0.293 0.251 0.307 0.367 0.293 0.251 0.307 0.367 | 0.636 0.559 0.618 0.669 0.891 0.858 0.896 0.928 O 1.374 1.354 1.402 1.447 1.374 1.354 1.402 1.447

Λ 0.954 0.919 0.963 1.000 0.954 0.919 0.963 1.000 G* 0.434 0.238 0.378 0.507 0.724 0.629 0.797 0.955 GZ 0.199 0.110 0.197 0.277 0.579 0.415 0.524 0.628 eÜ* 0.751 0.708 0.732 0.754 0.724 0.649 0.688 0.728 eÜZ 0.883 0.868 0.883 0.899 0.889 0.876 0.891 0.906 eÜ*∗ 0.907 0.864 0.895 0.926 0.505 0.500 0.529 0.558 eÜZ∗ 0.712 0.650 0.693 0.732 0.726 0.671 0.712 0.764

China (CN) East Asia (EA5)


� 0.601 0.499 0.637 0.787 0.601 0.499 0.637 0.787 | 0.479 0.443 0.480 0.517 0.788 0.754 0.791 0.833 O 1.476 1.468 1.490 1.514 1.476 1.468 1.490 1.514

Λ 0.922 0.846 0.905 0.971 0.922 0.846 0.905 0.971 G* 0.405 0.339 0.411 0.497 0.493 0.450 0.548 0.640 GZ 0.999 0.932 0.965 1.000 0.733 0.583 0.693 0.812 eÜ* 0.849 0.824 0.842 0.859 0.797 0.781 0.802 0.825 eÜZ 0.931 0.902 0.922 0.940 0.925 0.914 0.923 0.931 eÜ*∗ 0.715 0.644 0.708 0.761 0.746 0.726 0.783 0.837 eÜZ∗ 0.729 0.705 0.733 0.759 0.784 0.761 0.781 0.805

China (CN) Southeast Asia (SEA4)


� 0.916 0.812 1.020 1.209 0.916 0.812 1.020 1.209 | 0.844 0.808 0.862 0.902 0.603 0.579 0.618 0.663 O 1.592 1.519 1.559 1.603 1.592 1.519 1.559 1.603

Λ 0.927 0.861 0.920 0.991 0.927 0.861 0.920 0.991 G* 0.512 0.377 0.518 0.709 0.732 0.424 0.610 0.771 GZ 1.000 0.901 0.949 1.000 0.637 0.597 0.752 0.919 eÜ* 0.656 0.623 0.657 0.694 0.567 0.513 0.563 0.611 eÜZ 0.935 0.927 0.941 0.954 0.856 0.835 0.855 0.874 eÜ*∗ 0.745 0.664 0.744 0.813 0.648 0.523 0.643 0.732 eÜZ∗ 0.715 0.677 0.707 0.739 0.555 0.500 0.522 0.546

Notes: (i) The posterior distribution is obtained using the Metropolis-Hastings sampling algorithm based on 4

parallel chains of 50,000 draws, of which the first half was discarded as burn-in. The average acceptance rate for

each estimated model is as what follows: SEA4-EA5: 0.219; CN-EA5: 0.235; and CN-SEA4: 0.251. We impose

identical posteriors for �, O, and Λ across regions. (ii) SEA4 comprises Indonesia, Malaysia, the Philippines,

and Thailand weighted by total trades. (iii) EA5 comprises Japan, Hong Kong, Korea, Singapore, and Taiwan

weighted by total trades.

32

Table 3 Measuring average value added in gross export, and production fragmentation and upstreamness

Decomposition of value added in gross exports (%)

Connection with existing

measures

Measure of

Upstreamness

DVA in

direct

final

goods

export

DVA in intermediates

absorbed by foreign for

domestic use

DVA in intermediates export

shipped back to source Foreign VA

VAX VS1* VS �

Midstream Downstream Midstream Downstream Midstream Downstream

(i) (ii) (iii) (iv) (v) (vi) (vii)

SEA4-EA5

Southeast Asia 7.374 35.793 29.369 0.373 6.983 19.733 0.376 72.536 7.355 20.109 0.366

East Asia 17.633 4.132 1.089 39.053 3.126 26.052 8.916 22.853 42.179 34.968 1.206

CN-EA5

China 23.723 19.164 16.237 7.856 0.422 12.762 19.835 59.125 8.278 32.597 0.254

East Asia 11.426 7.761 5.754 30.731 11.781 23.656 8.891 24.941 42.512 32.547 1.306

CN-SEA4

China 35.839 4.323 2.917 9.307 10.580 11.907 25.125 43.080 19.888 37.032 0.537

Southeast Asia 28.751 15.918 7.624 11.041 1.876 15.433 19.358 52.293 12.917 34.790 0.371

Notes: (i) As a share of gross exports, VAX refers to domestic value added proposed by Johnson and Noguera (2012a, 2012b), and is a sum of (i), (ii), and (iii); VS1* is

reflected domestic value added, defined in Daudin et al. (2011) and responds partly to Hummels et al. (2001), and equals (iv) + (v); VS refers to foreign value added of

domestic exports as defined by Hummels et al. (2001), and is the sum of (vi) and (vii).

(ii) � = Ûw�∗Ûw .

(iii) SEA4 comprises Indonesia, Malaysia, the Philippines, and Thailand weighted by total trades.

(iv) EA5 comprises Japan, Hong Kong, Korea, Singapore, and Taiwan weighted by total trades.

33

Home

Foreign

Technology: �� = ß(, �)

Market: �� ≡ ��: + ��:;

��; = ß�; , �;

��; ≡ ��;: + ��;;

Technology: �* = ß��:, F�;:

Market: �* ≡ �*: + �*:;

�*; = ß+F�:; , ��;; -

�*; ≡ �*;: + �*;;

Technology: �Z = ß��*: , F*;:

Market: �Z ≡ _:: + �Z:; + #

�Z; = ß+F*:; , �*;; -

�Z; ≡ �Z;: + _;: + #;

Consumption

Consumption

Fig. 1. Structure of production and trade

Upstream: Invest to

accumulate capital and

hire labor to produce

intermediates

Midstream: Combine

domestic and imported

foreign intermediates to

produce intermediates

Downstream: Combine

domestic and imported

foreign intermediates to

produce final goods for

consumption and

investment

34

Fig. 2. Cross correlations

-20 0 20-0.4

-0.2

0

0.2

0.4

0.6GDP

-20 0 20-0.4

-0.2

0

0.2

0.4

0.6Consumption

-20 0 20-0.5

0

0.5

1Export

-20 0 20-0.5

0

0.5

1Import

-20 0 20-0.4

-0.2

0

0.2

0.4

0.6GDP

-20 0 20-0.4

-0.2

0

0.2

0.4Consumption

-20 0 20-0.5

0

0.5

1Export

-20 0 20-0.5

0

0.5Import

-20 0 20-0.4

-0.2

0

0.2

0.4

0.6GDP

-20 0 20-0.4

-0.2

0

0.2

0.4Consumption

-20 0 20-0.5

0

0.5

1Export

-20 0 20-0.5

0

0.5

1Import

Data Model

SEA4-EA5

CN-EA5

CN-SEA4

35

x-axis denotes period; y-axis indicates responses in percentage

Fig. 3. Dynamic response of GDP towards common and idiosyncratic positive TFP shock.

0 5 10 15 200.1

0.15

0.2

0.25

0.3

0.35

CN

0 5 10 15 20-0.1

0

0.1

0.2

0.3

0.4

EA

0 5 10 15 20-0.1

0

0.1

0.2

0.3

0.4

0 5 10 15 20-0.2

-0.1

0

0.1

0.2

0 5 10 15 20-0.1

0

0.1

0.2

0.3

SE

A

CN

0 5 10 15 20-0.15

-0.1

-0.05

0

0.05

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25

SEA

0 5 10 15 20-0.2

-0.1

0

0.1

0.2

0 5 10 15 20-0.1

-0.05

0

0.05

0.1

EA

Common shock Idiosyncratic shock

Response

Shock

36

x-axis denotes period; y-axis indicates responses in percentage

Fig. 4. Dynamic response of GDP towards common and idiosyncratic negative preference

shock.

0 5 10 15 20-0.1

-0.05

0

0.05

0.1

CN

0 5 10 15 20-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

EA

0 5 10 15 20-0.1

-0.08

-0.06

-0.04

-0.02

0

0 5 10 15 20-0.1

-0.05

0

0.05

0.1

0 5 10 15 20-0.3

-0.2

-0.1

0

0.1

SE

A

CN

0 5 10 15 20-0.15

-0.1

-0.05

0

0.05

0.1

0 5 10 15 20-0.3

-0.2

-0.1

0

0.1

SEA

0 5 10 15 20-1.5

-1

-0.5

0

0.5

0 5 10 15 20-0.4

-0.2

0

0.2

0.4

EA

Common shock Idiosyncratic shock

Shock

Response

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